3. Usando as propriedades das potências, calcule. a) 2^5cdot 2^3 d) (-3)^2cdot ((1)/(2))^2 g) (4^2)^3 b) (-8)^21cdot (-8)^-18 (10)^-2:(10)^3 h) (2^-3)^4 c) ((4)/(3))cdot ((4)/(3))^2 f) ((3)/(2))^3:((6)/(5))^3

a) $$2^{5}\cdot 2^{3} = 2^{5+3} = 2^{8} = 256$$

b) $$(-8)^{21}\cdot (-8)^{-18} = (-8)^{21-18} = (-8)^{3} = -512$$

c) $$(\frac {4}{3})\cdot (\frac {4}{3})^{2} = (\frac {4}{3})^{1+2} = (\frac {4}{3})^{3} = \frac {64}{27}$$

d) $$(-3)^{2}\cdot (\frac {1}{2})^{2} = 9 \cdot \frac {1}{4} = \frac {9}{4}$$

f) $$(\frac {3}{2})^{3}:(\frac {6}{5})^{3} = (\frac {3}{2})^{3} \cdot (\frac {5}{6})^{3} = \frac {27}{8} \cdot \frac {125}{216} = \frac {3375}{1728} = \frac {225}{128}$$

g) $$(4^{2})^{3} = 4^{2 \cdot 3} = 4^{6} = 4096$$

h) $$(2^{-3})^{4} = 2^{-3 \cdot 4} = 2^{-12} = \frac {1}{4096}$$

Resumindo, as respostas corretas são:
a) 256
b) -512
c) $$\frac {64}{27}$$
d) $$\frac {9}{4}$$
f) $$\frac {225}{128}$$
g) 4096
h) $$\frac {1}{4096}$$